Precise gravity or acceleration measurements are important in a wide array of technological fields. For example in the field of inertial navigation, precisely measured acceleration as a function of time may be used to accurately track the trajectory of a moving body such as a ship or aircraft. However, when attempting to precisely measure a pure acceleration, care must be taken to ensure that the measurement is not skewed by a change in the local gravitational field. This is because local accelerations are physically indistinguishable from local gravitational fields. This equivalence, first appreciated by Albert Einstein, and now known as Einstein's equivalence principle plagues any inertial navigation system that requires high precision. However, inertial measurements may be improved through the of a gravity gradiometer to help determine if any large local mass anomalies, such as mountains, are perturbing the local gravitational field and thus systematically affecting the local acceleration measurement.
Precise maps of local gravitational fields may be used to identify subsurface anomalies such as hydrocarbon reservoir or sub-surface bunkers. Such subsurface structures or anomalies may be uniquely identified from a noisy signal by a characterization of their local gravity gradient signatures.
The gravitational force between any two masses is inversely proportional to the square of the distance between them. Furthermore, the local gravity gradient is defined to be the change in the local gravitational field as a function of distance along the measurement axis of the gradiometer. As shown in FIG. 1A, the local gravitational field generated by the Earth presents a natural gradient along the z axis. To determine a local gravity gradient along the z-direction, e.g., to determine the local gravity gradient of the Earth, two local gravity measurements must be made, for example at a distance z apart. FIG. 1A shows the result of two such measurement denoted by gz1 and gz2. The one dimensional gravity gradient
      ∂          g      z            ∂    z  is determined by subtracting the two measurements and dividing by the distance between them:
            ∂              g        z                    ∂      z        =                    g                  z          ⁢                                          ⁢          2                    -              g                  z          ⁢                                          ⁢          1                      z  Gravity gradient measurements, being inherently differential measurements, are superior to simple acceleration/gravity measurements in noisy systems, especially where common mode noise may be effectively eliminated through the differencing procedure.
Local gravity, or equivalently, local acceleration may be measured in various ways. For example, cold atom interferometers may be used to measure the local acceleration. FIG. 1B shows an example of a known cold atom gradiometer for measuring the local acceleration experienced by pair of cold atom samples. The acceleration measurement is accomplished by exposing a sample of cold atoms to a sequence of optical pulses to cause the atoms to split and travel along two legs of an interferometer, not too dissimilar from what occurs in an optical interferometer. In the optical case, the light is best understood as an electromagnetic wave, while in the case of cold atoms, atoms are best understood as a matter-waves with wavelengths given by λ=h/p, where the wavelength λ of the matter wave is inversely proportional to the momentum of the atom and h is Plank's constant. Such a matter wave interferometer based on cold atoms is disclosed in M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, “Measurement of the Earth's Gravity Gradient with an Atom Interferometer-Based Gravity Gradiometer” Physical Review Letters 81, 971 (1998), a portion of which is summarized below in reference to FIG. 1B.
The apparatus of FIG. 1B includes two samples of cold atoms that are trapped and cooled in two separate magneto-optical traps. The magneto optical traps are formed from a frequency stabilized trapping laser beam 119 that is slightly red detuned from a cycling transition in the cloud of cold atoms. Typically, a complex optical system is required to generate the 12 trapping laser beams from the single trapping laser beam 119. The system (not shown) typically requires several beam splitters, mirrors, and polarization elements to generate six pairs of counter propagating trapping laser beams (shown in the drawing as arrows converging at the cold atom samples 106 and 104). The magnetic traps are separated spatially within separate vacuum chambers (not shown). The acceleration measurements are made using a (π/2-π-π/2) pulse sequence of stimulated two-photon Raman laser pulses. The two-photon Raman pulses drive the state of the atoms to oscillate in time between two atomic ground-state hyperfine levels, phenomena known as Rabi oscillations. As is known in the art, the three pulse (π/2-π-π/2) sequence results in an atom interferometer if the two Raman laser beams counter-propagate. In the system shown in FIG. 1B, the counter-propagating Raman laser beams are generated from a dual frequency beam 103 that propagates in free space to the polarizing beam splitter 105. The beams are then spilt by the polarizing beam splitter 105 with the beam having the first frequency ω1 propagating straight through beam splitting cube 105 and, therefore, immediately through both clouds of cold atoms. The beam having the second frequency ω2 is reflected off of beam splitter 105 and beam splitter 107 and then propagates parallel to the first beam to the mirrors 109 and 110 that redirect the second beam through the two clouds of cold atoms in a direction opposite to the propagation direction of the first beam.
The relative acceleration along the direction of the Raman beams of the two cold atom samples are measured by subtracting two atomic phase shifts that are measured using the two atom interferometers at each of the two locations 101 and 103. The atomic phase shifts are derived quantities that are obtained from the measured atom population in the ground state. (As described below, the number of atoms found in the ground state after the Raman pulse varies sinusoidally with the phase difference introduced in one leg of the interferometer due to, e.g., gravitational acceleration or rotation about an axis perpendicular to the plane of the interferometer.) The measured atom population is determined by way of resonance fluorescence. More specifically, a probe beam 117 tuned to resonance with a cycling transition is briefly pulsed on the atoms. Typically the probe beam 117 is a different beam from the Raman beam and is introduced into the system by way of beam splitter 107. Like Raman beam 103, the probe beam 117 is redirected by mirrors 109 and 110 so as to overlap the cold atom samples 106 and 104. The resulting fluorescence from the atoms is picked up by detectors 113 and 115. Using known and validated physical models, the number of atoms in the ground state may then be inferred from the amount of detected fluorescence.
As alluded to above, the number of atoms present in the ground state depends on the measured phase between the interferometer legs and may be found using the relation p=[1−cos Δφ(r)]/2, where P is the probability of an atom to be in the ground state as a function of the acceleration induced phase shift. For atoms accelerating at a rate g(r), Δφ(r)=({right arrow over (k)}1−{right arrow over (k)}2)·{right arrow over (g)}(r)T2, where T is the time between successive Raman beam pulses, and {right arrow over (k)}1 and {right arrow over (k)}2 are the propagation vectors for the Raman beams of frequency ω1 and ω2, respectively. Thus, by measuring the ground state populations, the phase difference Δφ(r), and thereby the projection of g(r) on the measurement axis may be determined. Furthermore, the acceleration gradient can then be determined by dividing the relative acceleration by the distance between the two locations where the acceleration measurements are made.
In view of the above, the gravity gradiometer shown in FIG. 1B is fairly complex. As can be seen in the Figure, several different laser sources are needed to create the 12 magneto-optical beams, the two Raman laser beams, and the fluorescence probe. Furthermore, the system described in FIG. 1B requires each magneto-optical trap to be housed in a separate vacuum chamber 121 and 123.
In addition, an example of inertial measurements based on cold atom interferometry is disclosed in U.S. patent application Ser. No. 12/921,519 (“the '519 application”). The interferometer of the '519 application is based on a magneto-optical trap that uses a single pyramidal retro-reflector for absolute acceleration/gravity measurements. The system of the '519 application cannot measure gravity gradients and is additionally sensitive to vibrational noise in the single pyramidal retro-reflector. Due to the equivalence principle any vibrational noise shows up as noise that is indistinguishable from the gravity signal.